Question

Consider a bond that has a coupon rate of 7%, three years to maturity, and is currently priced to yield 5%. Calculate the following:  Macaulay duration  Modified duration  Percentage change in price for a 1% increase in the yield to maturity

Answer 1

K = N

Bond Price =∑ [(Annual Coupon)/(1 + YTM)^k]     +   Par value/(1 + YTM)^N

k=1

K =3

Bond Price =∑ [(7*1000/100)/(1 + 5/100)^k]     +   1000/(1 + 5/100)^3

k=1

Bond Price = 1054.46

Period	Cash Flow	PV Cash Flow	Duration Calc
0	($1,054.46)
1	70.00	66.67	66.67
2	70.00	63.49	126.98
3	1,070.00	924.31	2,772.92
		Total	2,966.57

Macaulay duration=

= 2966.57/1054.46 = 2.81

Modified duration = Macaulay duration/(1+YTM)

=2.81/(1+0.05) = 2.68

with 1% increase in YTM price is:

Modified duration prediction = -Mod_Duration*Yield_Change

=-2.68*1

=-2.68%